### Abstract

The k-ary n-dimensional shuffle-exchange directed network S(k, n) consists of k^{n} nodes such that each node is represented as an k-ary n-tuple vector, a_{1}a_{2}···a_{n}, where a_{i} is in [0, k-1]. Node a_{1}a_{2}···a_{n} is adjacent to node a_{2}a_{3}···a_{n}a_{1} (one shuffle link) and k-1 other nodes a_{1}a_{2}···a_{n-1}b, where b∈[0, k-1] and b≠a_{n} (k-1 exchange links). S(k, n) have been widely used as topologies for VLSI networks, parallel architectures, and communication systems. However, since S(k, n) does not exist for the number of nodes between k^{n} and k^{n+1}, Liu and Hsu have recently proposed a class of digraphs GS(k, N), which generalized S(k, n) to any number N of nodes. They also showed that GS(k, N) retains all the nice properties of S(k, n). In this paper, we survey these combinatorial properties and study Hamiltonian properties of GS(k, N). In particular, we have successfully obtained Hamiltonian circuit for GS(k, k(k+1)) for any k>2.

Original language | English (US) |
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Pages (from-to) | VI-157-VI-160 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | 6 |

State | Published - Jan 1 1999 |

Event | Proceedings of the 1999 IEEE International Symposium on Circuits and Systems, ISCAS '99 - Orlando, FL, USA Duration: May 30 1999 → Jun 2 1999 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*,

*6*, VI-157-VI-160.